Метод решения краевой упругопластической задачи о растяжении полосы с концентраторами напряжений с учетом локальных областей пластического разупрочнения материала

Abstract

The way of solution of the coupled boundary value problem of solid body deformation for the case of a plastically softening material is offered. The strain and stress fields obtained by the simulated undamaged construction behavior modeling under the action of fictitious forces are used as basic data for calculation. The equivalence of simulated undamaged medium strains and real medium strains is supposed. At each point of construction the damage parameter $\omega$ is calculated by means of constitutive relations of the endochronic plasticity theory. This damage parameter associates the components of the true stress tensor $\sigma_{ij}$ of simulated undamaged medium and the engineering stress tensor $\sigma^0_{ij}$ of real medium by $\sigma^0_{ij}=\sigma_{ij}/(1+\omega)$. Using the tensor $\sigma^0_{ij}$ we can calculate the generalized forces of real construction. The problems of tension of the plates weakened with centric circular hole and semicircular notches are solved and the necessary experiments are conducted. The strain and true stress fields are obtained by numerical calculation at the finite element analysis software and are used for the engineering stress of real construction computation according to the foregoing expression. Softening plasticity domains are plotted. It is found that at the moment before failure the stage of post critical deformation is implementing in the region of stress concentration, although the curve “total displacement - axial force” corresponds to the stage of plastic hardening.